Honestly just going by Ebert's opinion here, who felt that her taking the mental illness seriously clashed with the campy tone. I've never actually seen that film. We could go the other way too, Turner's serious performance in a serious movie.
actually i never took it as campy. at first glance it looks campy, but it isn't. she plays a very appreciated person in the neighbourhood, seems very caring. and there is something that triggers her, and from point you more and more see he dark side.
The virtual camera position slowly moves from the front, how she looks like to others, then slowly towards her dark side. and also how the kifs & some around her exploit the serial mom thing is a nice critique on americas obsession sometimes with (serial) killers.
it s a dark comedy, but it is a very waters movie, means you really have to see it a few times to get all the nuances. and turner did a great job switching between the seemingly caring mom & neighbour and the psychopath at the flick of a switch.
and of course some of it was very over the top, but that is typically waters (and it is a dark comedy after all). and the ending especially where she breaks down the 3rd wall for a moment, and show the real psychoness.
and also remember it may be a dark comedy, but it is based on something that really happened .
and on your citing of ebert, here a quote from wiki on it:
Roger Ebert awarded it an average two stars (out of a possible four) finding some of Waters' satire effective but feeling that Kathleen Turner's decision to portray her character's mental illness with realism instead of in a campy fashion, while brave, made the character difficult to laugh at, writing, "Watch Serial Mom closely and you'll realize that something is miscalculated at a fundamental level. Turner's character is helpless and unwitting in a way that makes us feel almost sorry for her—and that undermines the humor. She isn't funny crazy, she's sick crazy."
turner is portraying a psychopath, that is pretty serious, and should treated that way. it is more that the viewer is made to think they are watching a dark comedy, but slowly but surely you discover this is no laughing matter, the movie pretty much deceives the viewer into this the same way psychopaths deceive people into believing they are normal. i think ebert just didn't get the movie. the movie underneath the veneer of comedy never was meant to be funny, and is actually pretty seriousm and this clashing of what it really is probably what made him feel that something is miscalculated. Waters really managed that fake sense of safety that helps psychos to lure their victims, right up to the end with the 'oh shit' moment. the first time you watch it, you watch as a comedy, the 2nd time that feeling is already far less, watching it the 3rd time you realise it is not comedy, it is the fascination of watching an ongoing trainwreck.
and since you haven't seen the movie, i seriously advise watching it.
edit: what eberts essentially says, he wanted the movie to look more like scary movie, and that he doesn't like it because it makes him use his brain